Waterloo Mathematics
Grade 7 Patterning and Algebra: Algebraic Expressions
Classmates solve 18 different problems that are mostly word problems that apply algebraic expressions. They draw different combinations of masses on a scale that would balance. They also simplify expressions and solve for x in a number...
Curated OER
Graphs and Functions
Middle schoolers describe plotting functions on the Cartesian coordinate plane. They solve functions on paper and using an online tool to plot points on a Cartesian coordinate plane creating lines and parabolas.
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Reading Graphs
Working independently or in teams, your class practices connecting graphs, formulas and words. This lesson plan includes a guided discussion about distance vs. time graphs and looking at how velocity changes over time.
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I Can Do This! Systems of Equations
Students solve systems of 2-by-2 linear equations using tables,
graphs and substitution. In small groups, classmates work together to discover strategies for solving equations. They use a calculator to graphically represent their answers.
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The Power of Algebra
First graders explore patterns. They look for patterns in number problems and use algebra as a means of solving general problems. Students devise a strategy to solve the number problem.
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Tilted Squares and Right Triangles
Students investigate squares. They generate patterns from structured situations and find a rule for the general term and express it using words and symbols. Students generate patterns from a rule and substitute values and formulas.
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Marcy's Dots
Students identify the pattern changes that could occur in a series using pictures with dots. They use the patterns on the worksheets to have a context to describe pattern in words. Students look to find the linear, quadratic, or...
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Simple Sequence
Students identify the nth term in a sequence. In this algebra lesson, students generate sequences given the formula for each sequence. They find the formula given the sequence.
Ms. Amber Nakamura's Mathematics Website
Algebra Project
What would your dream house look like? A cottage? A medieval castle? High schoolers enrolled in Algebra design the perfect house while using slopes to write equations for various aspects of the project.
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Functions and the Vertical Line Test
Learners examine functions and function notation. They use computer activities to discover how to graph functions, and conduct a vertical line test. Students describe spatial relationships using coordinate geometry.
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Cups and Cubes
Third graders explore the use of cups and counters as a model to analyze the effects of operations. They create and use a rule to create a sequential pattern and use cups and cubes to model the relationship.
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What Configurations Work to Light a Bulb?
Learners explore simple electrical circuits. Students experiment, using different configurations, to determine what is necessary to compeete a circuit. Learners observe similarities between arrangements that work and differences in...
02 x 02 Worksheets
Inverse Variation
Discover an inverse variation pattern. A simple lesson plan design allows learners to explore a nonlinear pattern. Scholars analyze a distance, speed, and time relationship through tables and graphs. Eventually, they write an equation to...
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Pizza Toppings 2
Students explore possible combinations of items. They devise and use problem solving strategies to explore situations mathematically. They examine using linear and quadratic patterns to solve combination problems. From a given...
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Investigation - Looking For Triangles
Seventh graders investigate a series of triangles, looking for patterns and generalizing what they have found. They analyze the pattern data and organize it into a table and graph. Students identify the relationship and discover the rule...
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Data and Scientific Graphs
Learners conduct experiments and graph their data. In this statistics instructional activity, students collect data and graph it on a coordinate plane. They analyze the data looking for patterns and they discuss their findings with the...
American Statistical Association
Scatter It! (Predict Billy’s Height)
How do doctors predict a child's future height? Scholars use one case study to determine the height of a child two years into the future. They graph the given data, determine the line of best fit, and use that to estimate the height in...
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Arithmagons
Fifth graders explore patterns and relationships among the numbers that form arithmagons. They create and attempt different rules that can be used to solve arithmagons. Students use linear algebra to solve arithmagons.
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The Why and How of General Terms
Sixth graders find the recurrence relation for simple sequences
construct tables of values for a pattern. They find the value of the general term of a sequence algebraically.
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Introduction to Solving Quadratic Equations by Factoring
Students solve quadratic equations. In this algebra lesson, students factor and graph linear and quadratic functions. They identify the standard and linear form of each equation.
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Moving Straight Ahead
Students analyze the relationship between speed, time and distance. In this math lesson, students plan a school trip. Students determine the efficiency and cost effectiveness of a trip.
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Four Fours Challenge
Second graders look at the number patterns created when tins are stacked in different arrangements. The aim of the unit is for students to keep track of the numbers involved by drawing up a table of values. They are then encouraged to...
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Square and Triangular Numbers
Students use equations to represent practical situations. They solve linear equations and quadratic equations. The use of problem solving strategies is also developed.
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Square Milk Bottle Crates
Students attempt a problem that Students has the potential to have more than one solution. Hence the problem is accessible to a wide range of students. The problem is essentially about finding patterns and this is typical of a number of...